Volume 23 , Issue 4 , PP: 350-357, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
P. Prabakaran 1 , Bilal Abdallah 2 * , Turayeva Dinara Tulkunovna 3
Doi: https://doi.org/10.54216/IJNS.230427
The main objective of this article is to study the inverse of invertible symbolic 3-plithogenic real square matrices using the concept of adjoints and characteristic polynomials. Also, the symbolic 3-plithogenic version of Cayley-Hamilton theorem was proved and provided enough examples to enhance understanding.
Symbolic 3-plithogenic matrix , symbolic 3-plithogenic adjoint , symbolic 3-plithogenic determinant , symbolic 3-plithogenic inverse.
[1] Adeleke, E. O., Agboola, A. A. A., and Smarandache, F., “Refined neutrosophic rings II”, International Journal of Neutrosophic Science, vol. 2, pp. 89-94, 2020.
[2] Abobala, M., “On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations”, Journal Of Mathematics, Hindawi, 2021.
[3] Abobala, M., “On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations”, Mathematical Problems in Engineering, Hindawi, 2021.
[4] Abobala, M., Hatip, A., Olgun, N., Broumi, S., Salama, A,A., and Khaled, E, H., “The Algebraic Creativity In The Neutrosophic Square Matrices”, Neutrosophic Sets and Systems, Vol. 40, pp.1-11, 2021.
[5] Abobala, M., “On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations”, Journal of Mathematics, Hindawi, 2021.
[6] Abobala, M., “A Study of Nil Ideals and Kothe’s Conjecture in Neutrosophic Rings”, International Journal of Mathematics and Mathematical Sciences, Hindawi, 2021.
[7] Abuobida Mohammed A. Alfahal, Yaser Ahmad Alhasan, Raja Abdullah Abdulfatah, Arif Mehmood, Mustafa Talal Kadhim, “On Symbolic 2-Plithogenic Real Matrices and Their Algebraic Properties”, International Journal of Neutrosophic Science, Vol. 21, PP. 96-104, 2023.
[8] Albasheer, O., Hajjari., A., and Dalla., R., “On The Symbolic 3-Plithogenic Rings and Their Algebraic Properties”, Neutrosophic Sets and Systems, Vol 54, 2023.
[9] Ali, R., Hasan, Z. “An Introduction to the Symbolic 3-Plithogenic Vector Spaces”, Galoitica: Journal of Mathematical Structures and Applications, 2023, 6, 8-12.
[10] Ali, R.; Hasan, Z., “An Introduction to the Symbolic 3-Plithogenic Modules”, Galoitica: Journal of Mathematical Structures and Applications, 2023, Vol 6, 13-17.
[11] Kandasamy, W. B. V., and Smarandache, F., “Some Neutrosophic Algebraic Structures and Neutrosophic n-Algebraic Structures”’, (Arizona: Hexis Phoenix), 2006.
[12] Khaldi, A., Ben Othman, K., Von Shtawzen, O., Ali, R., and Mosa, S., “On Some Algorithms for Solving Different Types of Symbolic 2-Plithogenic Algebraic Equations”, Neutrosophic Sets and Systems, Vol 54, 2023.
[13] Malath F. Alaswad, “On the Neutrosophic Characteristic Polynomials and Neutrosophic Cayley-Hamilton Theorem”, International Journal of Neutrosophic Science, Vol. 18, 2022, PP. 59-71.
[14] Merkepci, H., and Abobala, M., “On The Symbolic 2-Plithogenic Rings”, International Journal of Neutrosophic Science, 2023.
[15] Merkepci, H., and Rawashdeh, A., “On The Symbolic 2-Plithogenic Number Theory and Integers ”, Neutrosophic Sets and Systems, Vol 54, 2023.
[16] Merkepci, H., “On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4- Plithogenic Real Square Matrices”, Symmetry, 2023.
[17] Othman, B.K., “On Some Algorithms for Solving Symbolic 3-Plithogenic Equations”, Neoma Journal of Mathematics Computer Science 2023
[18] Rawashdeh, A, “An Introduction to the Symbolic 3-plithogenic Number Theory”, Neoma Journal of Mathematics Computer Science, 2023.
[19] Smarandache, F., “Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)”, Neutrosophic Sets and Systems, vol. 53, 2023.
[20] Smarandache, F., “Introduction to Neutrosophic Statistics”, USA: Sitech and Education Publishing, 2014.
[21] Taffach, N., “An Introduction to Symbolic 2-Plithogenic Vector Spaces Generated from The Fusion of Symbolic Plithogenic Sets and Vector Spaces”, Neutrosophic Sets and Systems, Vol 54, 2023.
[22] Taffach, N., and Ben Othman, K., “An Introduction to Symbolic 2-Plithogenic Modules Over Symbolic 2-Plithogenic Rings”, Neutrosophic Sets and Systems, Vol 54, 2023.